Comparison principle of very weak solutions for nonhomogeneous elliptic equations. (English) Zbl 1463.35134
Summary: Under some suitable assumptions, a comparison principle of very weak solutions for quasi-linear elliptic equation \(-{\mathrm{div}}A(x, \nabla u) = f(x, u)\) is given by using McShane extension theorem to construct the Lipschitz continuous test function, and the corresponding results of some homogeneous equations are generalized.
MSC:
35B51 | Comparison principles in context of PDEs |
35D30 | Weak solutions to PDEs |
35J62 | Quasilinear elliptic equations |